Cardiovascular Engineering

, Volume 7, Issue 4, pp 162–171 | Cite as

Pressure Phase-plane Based Determination of the Onset of Left Ventricular Relaxation

Original Paper


Contraction–relaxation coupling is often characterized in terms of its effects on contraction or relaxation parameters, such as the time-constant of isovolumic relaxation (τ). While thermodynamics-based LV function characterization methods exist, landmark relaxation-onset determination studies used surgical methods. One classic, open-chest preparation study found that relaxation-onset occurs during early ejection, i.e. 34% of systolic time, T SYS, defined as the time from end-diastolic pressure to peak negative dP/dt. Because ventricular pumping is a steady state system, the laws of thermodynamics and nonlinear dynamics require that energy generation (during contraction) and energy utilization (during relaxation) must be balanced in a time-averaged (steady-state) sense. We calculated both energy generation and energy utilization, via novel pressure phase-plane (PPP) based parameters, including isovolumic stiffness analogs, in 29 subjects, 20 cardiac cycles per subject (580 beats). Results in control subjects show that relaxation-onset occurs near or prior to 34% of T SYS. In hearts with sever dysfunction including prolonged τ, relaxation-onset commences after 50% of T SYS (p < 0.05). We conclude that PPP-based analysis can characterize relaxation-onset in vivo in thermodynamic and nonlinear dynamics terms without requiring an open-chest preparation, and may facilitate characterization of cellular mechanisms of relaxation-onset at the organ system level.


Hemodynamics Diastole Relaxation Pressure phase plane Limit cycle 



We thank the staff of the Cardiac Catheterization Laboratory at Barnes Jewish Hospital for assistance in data acquisition and Leonid Shmuylovich for helpful comments in manuscript preparation. Helpful comments regarding energy flux by Professor Guy Genin is gratefully acknowledged. CSC is currently at the Department of Molecular and Cellular Biology, University of Arizona, Tucson AZ. Supported in part by the American Heart Association Heartland Affiliate (0610042Z, CSC), Whitaker Foundation, National Institutes of Health (HL54179, HL04023 SJK), the Barnes-Jewish Hospital Foundation and the Alan A. and Edith L. Wolff Charitable Trust.


  1. Allan DG, Kurihara S. The effects of muscle length on intracellular calcium transients in mammalian cardiac muscle. J Physiol (London). 1982;327:79–94.Google Scholar
  2. Baker GL, Gollub JP. Chaotic dynamics, an introduction. New York: Cambridge University Press; 1990.Google Scholar
  3. Brutsaert DL, Rademakers FE, Sys SU. Triple control of relaxation: implications in cardiac disease. Circulation. 1984;69:190–6.PubMedGoogle Scholar
  4. Campbell KB, Taheri H, Kirkpatrick RD, Burton T, Hunter WC. Similarities between dynamic elastance of left ventricular chamber and papillary muscle of rabbit heart. Am J Physiol. 1993;264:H1926–41.PubMedGoogle Scholar
  5. Chung CS, Ajo DM, Kovács SJ. The isovolumic pressure to early rapid filling decay rate relation: model-based derivation and validation via simultaneous catheterization-echocardiography. J Appl Physiol. 2006a;100:528–34.PubMedCrossRefGoogle Scholar
  6. Chung CS, Strunc A, Oliver R, Kovács SJ. The diastolic ventricular-vascular stiffness and relaxation relation: elucidation of coupling via pressure phase-plane derived indexes. Am J Physiol Heart Circ Physiol. 2006b;291:H12415–23.CrossRefGoogle Scholar
  7. Camacho SA, Brandes R, Figueredo VM, Weiner MW. Ca2+ transient decline and myocardial relaxation are slowed during low flow ischemia in rat hearts. J Clin Invest. 1994;93:951–7.PubMedGoogle Scholar
  8. Eucker SA, Lisauskas J, Courtois MR, Kovács SJ. Analysis of left ventricular hemodynamics in physiological hyperspace. J Appl Physiol. 2002;92:323–30.PubMedGoogle Scholar
  9. Eucker SA, Lisauskas JB, Singh J, Kovács SJ Jr. Phase plane analysis of left ventricular hemodynamics. J Appl Physiol. 2001;90:2238–44.PubMedGoogle Scholar
  10. Gao WD, Perez NG, Marban E. Calcium cycling and contractile activation in intact mouse cardiac muscle. J Physiol. 1998;507:175–84.PubMedCrossRefGoogle Scholar
  11. Granzier HL, Irving TC. Passive tension in cardiac muscle: contribution of collagen, titin microtubules, and intermediate filaments. Biophys J. 1995;68:1027–44.PubMedCrossRefGoogle Scholar
  12. Hinken AC, Solaro RJ. A dominant role of cardiac molecular motors in the intrinsic regulation of ventricular ejection and relaxation. Physiology. 2007;22:73–80.PubMedCrossRefGoogle Scholar
  13. Johnson LL, Ellis K, Schmidt D, Weiss MB, Cannon PJ. Volume ejected in early systole a sensitive index of left ventricular performance in coronary artery disease. Circulation. 1975;52:378–89.PubMedGoogle Scholar
  14. Kass DA. Assessment of diastolic dysfunction. Cardiol Clin. 2000;18(3):571–86.PubMedCrossRefGoogle Scholar
  15. Kass DA, Bronzwaer JG, Paulus WJ. What mechanisms underlie diastolic dysfunction in heart failure? Circ Res. 2004;94:1533–42.PubMedCrossRefGoogle Scholar
  16. Karamanoglu M, Kovács SJ. Thermodynamic phase plane analysis of ventricular contraction and relaxation. Biomed Eng Online. 2004;5:6.CrossRefGoogle Scholar
  17. Katz AM, Lorell BH. Regulation of cardiac contraction and relaxation. Circulation. 2000;102:IV69–74.PubMedGoogle Scholar
  18. Lisauskas JB, Singh J, Bowman AW, Kovács SJ Jr. Chamber properties from transmitral flow: prediction of average and passive left ventricular diastolic stiffness. J Appl Physiol. 2001;91:154–62.PubMedGoogle Scholar
  19. Matsubara H, Takaki M, Yasuhara S, Arki J, Suga H. Logistic time constant of isovolumic relaxation pressure-time curve in the canine left ventricle. Circulation 1995;92:2318–26.PubMedGoogle Scholar
  20. Rosen BD, Gerber BL, Edvardsen T, Castillo E, Amado LC, Nasir K, Kraitchman DL, Osman NF, Bluemke DA, Lima JAC. Late systolic onset of regional LV relaxation demonstrated in three dimensional space by MRI tissue tagging. Am J Physiol Heart Circ Physiol. 2004;287:H1740–6.PubMedCrossRefGoogle Scholar
  21. Sagawa K, Maughan L, Suga H, Sunagawa K. Cardiac contraction and the pressure-volume relationship. New York: Oxford University Press, 1988. p. 5, 107–9.Google Scholar
  22. Solomon SB, Nikolic SD, Frater RWM, Yellin EL. Contraction–relaxation coupling: determination of the onset of diastole. Am J Physiol. 1999;277:H23–7.PubMedGoogle Scholar
  23. Strogatz SH. Nonlinear dynamics and Chaos. Cambridge MA: Perseus Publishing; 2000.Google Scholar
  24. Sugawara M, Uchida K, Kondoh Y, Magosaki N, Niki K, Jones CJ, Sugimachi M, Sunagawa K. Aortic blood momentum—the more the better for ejecting heart in vivo? Cardiovasc Res. 1997;33:433–46.PubMedCrossRefGoogle Scholar
  25. Wang Z, Jalali F, Sun Y-H, Wang J-J, Parker KH, Tyberg JV. Assessment of left ventricular diastolic suction in dogs using wave-intensity analysis. Am J Physiol Heart Circ Physiol. 2005;288:H1641–51.PubMedCrossRefGoogle Scholar
  26. Weiss J, Frederiksen JW, Weisfeldt ML. Hemodynamics determinant of the time course of fall in canine left ventricular pressure. J Clin Invest. 1976;58:751–60.PubMedCrossRefGoogle Scholar
  27. Wiggers CJ. Studies on the consecutive phases of the cardiac cycle I, the duration of the consecutive phases of the cardiac cycle. Am J Physiol. 1921;56:415–38.Google Scholar
  28. Wu Y., Yu Y, Kovács SJ. Contraction–relaxation coupling mechanism characterization in thermodynamic phase plane: normals vs impaired left ventricular ejection fraction. J Appl Physiol. 2007;102:1367–73.PubMedCrossRefGoogle Scholar
  29. Yoshida T, Othe N, Narita H, Sakata S, Wakami K, Asada K, Miyabe H, Saeki T, Kimura G. Lack of inertial force of late systolic aortic flow is a cause of left ventricular isolated diastolic dysfunction in patients with coronary artery disease. J Am Coll Cardiol. 2006;45:983–91.CrossRefGoogle Scholar
  30. Zhang W, Chung CS, Kovács SJ. Derivation and left ventricular pressure phase plane based validation of a time dependent isometric crossbridge attachment model. Cardiovasc Eng. 2006;6:132–44.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Cardiovascular Biophysics Laboratory, Cardiovascular DivisionWashington University Medical CenterSt. LouisUSA

Personalised recommendations